Find all functions $ f: \mathbb{R}^{+}\rightarrow \mathbb{R}$ that satisfy: $ f(x)f(y)=f(xy)+2005 \left( \frac{1}{x}+\frac{1}{y}+2004 \right)$ for all $ x,y>0.$
Source: Ukraine 2005 grade 10
Tags: function, algebra proposed, algebra
Find all functions $ f: \mathbb{R}^{+}\rightarrow \mathbb{R}$ that satisfy: $ f(x)f(y)=f(xy)+2005 \left( \frac{1}{x}+\frac{1}{y}+2004 \right)$ for all $ x,y>0.$